Erik Kusch, PhD Student

Department of Biology

Section for Ecoinformatics & Biodiversity

Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)

Aarhus University

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 1

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 2

“The distribution with the largest

entropy the most consistent with

stated assumptions.”

Not knowing anything, we bet on the flattest distribution.

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[Study Group] Bayesian Statistics with the Rethinking Material 3

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 4

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[Study Group] Bayesian Statistics with the Rethinking Material 5

Binomial

 Constraint:

 “Expected value

is high”

Poisson

 Constraint:

 “Expected value

is low”

Exponential

 Core function

Same proportional rate

of change across entire

distribution

Gamma

 Multiple things have

to happen for the

outcome to transpire

 Constraint:

 “Events sum up

to form outcome”

Normal

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 6

Do not(!) eye-ball outcome distribution from the histogram of the observed outcomes.

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[Study Group] Bayesian Statistics with the Rethinking Material 7

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[Study Group] Bayesian Statistics with the Rethinking Material 8

Variables interact on outcome scale as a consequence of compression of scale.

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 9

 “When a lizard is dead due to

cold temperatures, food

availability won’t matter to it”

 Effect of food is conditional on

effect of temperature

 This happens even when we

don’t specify an interaction

effect in our model

Finding the slope between an

outcome and a response is tricky

beyond the basic linear regression

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 10

 E(y)… Expected

mean value

 var(y)… Variance

of outcome

05/03/2021

[Study Group] Bayesian Statistics with the Rethinking Material 11

Link between log-odds

and probability scale we

are interested in as our

outcome

Globe toss example - Probability of water:

The logit link is just one out of many (e.g. probit, log-

log) to be used with binomial distributions.